Encoding apparatus and method, recording medium and program

ABSTRACT

A code sequence is encoded using a code conversion table in which the parity of the code sequence varies until the code states become equal to each other. The code word assignment used in this code conversion table is such that the decoded code word constraint length is 3 blocks and q 0 ≠q 1  for an arbitrary information sequence is satisfied even if a DC control bit is inserted at any of the first and second bits of an information word. For example, code states s 0  and s 1  when information sequences d 0  and d 1  resulted from insertion of provisional DC control bits  1  and  0  inserted at the top of an information sequence “1, 1, 0, 0, 0, 1, 0” are encoded starting with a state 3 according to a predetermined code conversion table are equal to each other, namely, s 0 =s 1 =6, in a third block, and two&#39;s complement q 0  of a sum of code sequences c 0  up to a time when the code states are equal to each other is “0” while two&#39;s complement q 1  of a sum of code sequences c 1  up to that time is “1”. That is, the condition that q 0 ≠q 1  is met. The present invention can be applied to a recorder/player or encoder.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a coding apparatus andmethod, recording medium and a program, and more particularly to acoding apparatus and method, recording medium and a program, suitablefor use in converting an m-bit information word continuously into ann-bit code word with DC control bits for DC control of a code sequencebeing inserted in a sequence of information.

This application claims the priority of the Japanese Patent ApplicationNo. 2003-079556 filed on Mar. 24, 2003, the entirety of which isincorporated by reference herein.

2. Description of the Related Art

Many of various types of recorder/players and communications devices aredesigned for a reduced rate of errors, caused by coding of inputinformation, of digitally transmitted information.

Referring now to FIG. 1, there is schematically illustrated in the formof a block diagram a digital signal processing circuit included in atypical conventional recorder/player indicated with a reference 1.

As shown, the digital signal processing circuit of the recorder/player 1includes an encoder 11. The encoder 11 encodes an information sequencecontinuously supplied into a ratio of m:n (m is data bit length beforecoding, and n is a data bit length after coding) to generate a sequenceof binary recording codes. It should be noted here that “m”, “n”, and“m-n” will be referred to as “information word length”, “code wordlength” and “code rate” or “coding rate”, respectively.

The digital signal processing circuit includes also a recording/playbackunit 12. The recording/playback unit 12 is composed of a magnetic head,optical pickup, control circuit to control the driving of the magnetichead and optical pickup, etc. to records a recording code supplied fromthe encoder 11 to a recording medium (not shown). Also, therecording/playback unit 12 reads a signal from the recording medium, andoutputs a reproduced analog wave to an analog equalizer 13 also includedin the digital signal processing circuit. The analog equalizer 13equalizes the reproduced wave from the recording/playback unit 12 to apredetermined target equalization characteristic.

The digital signal processing circuit includes also an A-D converter 14.The A-D converter 14 converts the supplied equalized signal into adigital read signal. As shown, the A-D converter 14 includes a PLL(phase-locked loop). This PLL may be a hybrid digital PLL that makesonly a phase error detection in a digital section thereof or afull-digital PLL that makes both a phase error detection and a signalsynchronization in a digital section thereof.

Also, in case the equalization by the analog equalizer 13 is notsufficient, a digital equalizer may be provided between the A-Dconverter 14 and a code detector 15 also included in the digital signalprocessing circuit. It should be noted that in this case, a lowpassfilter may be provided in place of the analog equalizer 13.

The above code detector 15 is supplied with a digital read signal(equalize signal) and converts it into a code (namely, it detects acode). Recently, it has become a common way to use a soft-decisiondetector such as a Viterbi detector or the like for the code detector15. A decoder 16 also included in the digital signal processing circuitis supplied with a detection code continuously supplied, decodes it intoa detection in formation in a ratio of n:m, and outputs the detectioninformation as a sequence of detection information.

As shown in FIG. 1, various codes are used in practice in the codingeffected in the encoder 11. Many different types of recorder/playersadopt, for example, a (d, k) RLL (run-length limited) code in which d isa minimal number of 0's between 1's in a code sequence (minimum run) andk is a maximum number of 0's between 1's (maximum run) as in the NRZI(nonreturn-to-zero-inverted recording) modulation in which a recordedrectangular wave is inverted on one bit.

Especially in many optical players using an optical pickup for readingsignals, a minimum run-length limited code with a minimum run d of morethan one “0” is used to reduce the deterioration in quality of a readsignal, due to the nonlinearity of the optical pickup. The compact disk(CD) recorder/players and music-playing mini disk (MD) recorder/players,having been popular, employ a (2, 10) RLL code of 8/17 in coding ratiocalled “EFM (eight to fourteen modulation)”, and the MD DAT2 used in thedata-recording mini disk recorder/players adopt a (1, 7) RLL code of 2/3in coding rate, for example.

Also, the (d, k) RLL code is not adopted only in the recorder/players. A(1, 13) RLL code of 2/3 in coding rate is employed in the radiocommunications device using an infrared ray called “IrDA-VFIr (infrareddata association, very fast infrared), for example.

Of the (d, k) RLL codes, the EFM code is a fixed-length code and the (1,7) RLL code is a variable-length code. Generally, the variable-lengthcode is encoded based on either a look-ahead code conversion table or afinite-state code conversion table.

FIGS. 2 and 3 show the well-known look-ahead code conversion tables ofthe (1, 7) RLL codes (by Cohn-Jacoby-Bates). FIG. 2 shows a basic codeconversion table, and FIG. 3 shows an irregular code conversion table.An information sequence is encoded according to the basic codeconversion table in FIG. 2. When an information sequence as listed inthe irregular code conversion table in FIG. 3 is supplied, the irregularcode conversion table in FIG. 3 is preferentially applied to encode theinformation sequence (see the U.S. Pat. No. 4,337,458 to M. Cohn, G.Jacoby and C. Bates, for example).

On the assumption that one block is a minimum unit of coding (equivalentto 2 bits of input information or 3 bits of code in the basic codeconversion table in FIG. 2, for example), the encoder 11 that encodesinformation according to the code conversion tables in FIGS. 2 and 3 hasto look ahead an information sequence for one block in order to encodeinformation. Also, the look-ahead code conversion tables in FIGS. 2 and3 can be converted into finite-state code conversion tables,respectively, by re-assigning, to an information word, a code wordhaving been made to lag behind the information word by the same amountas a necessary look-ahead amount for the encoder 11.

Note here that the above “re-assignment of a code word made to lagbehind an information word by one block” is to assign a code work 001 toan information word 00 while a preceding information word is 10 sincetwo code words 001 and 000 are assigned to two information words 10 and00, respectively, as in FIG. 3.

FIG. 4 shows a finite state-type 5-state code conversion table for (1,7) RLL codes converted according to the look-head code conversion tablesin FIGS. 2 and 3. In FIG. 4, three bits shown before a slash (/)indicate a code word and a figure shown after the slash indicates atransition.

That is, the finite-state code conversion table in FIG. 4 is derivedfrom assignment of a 3-bit code word made to lag one block to aninformation word each of 2 bits in the look-ahead code conversion tablesin FIGS. 2 and 3 (see the article “The Power Spectrum ofRun-length-Limited Codes” by A. Gallopoulos, C. Heegard and P. Siegel,IEEE Trans. on Com., Vol. 37, No. 9, pp. 906-917, September 1989, forexample).

In case the encoder 11 has encoded information according to thelook-ahead code conversion tables in FIGS. 2 and 3, it can output only acode word delayed one block in relation to a code word assigned to aninput information word by one block for looking ahead the informationword. Also, in case the encoder 11 has encoded information according tothe finite-state code conversion table 4, it is necessary to look aheadany information word. However, the finite-state code conversion table inFIG. 4 is different from the code conversion tables in FIGS. 2 and 3 inthat a code word delayed one block is assigned to an information word.

That is, a code sequence resulted from encoding an information sequenceaccording to the look-ahead code conversion tables in FIGS. 2 and 3 willbe identical to a code sequence resulted from encoding according to thefinite-state code conversion table in FIG. 4. Therefore, the look-aheadcode conversion table and finite-state code conversion table appear topresent different codes, respectively, but they are different only innotation of a coding rule from each other. However, on the assumptionthat the internal circuit of the encoder 11 is constructed in faithfulaccordance with the coding rule of the code conversion tables, theencoder 11 will be different in circuit construction from each otherdepending upon which the code conversion table adopted is, a look-aheador finite state-type one.

Also, in case the code is not of a variable length but of a fixedlength, the code conversion table is of the finite state type alonesince an information sequence has not to be looked ahead. It can bediscriminated depending upon which the same code word is assigned to, aplurality of information words or a single information word, whether acode represented according to the finite-state code conversion table isa variable-length one or a fixed-length one.

Also, although the look-ahead code conversion table has to be designedby a heuristic approach, the finite-state code conversion table cantheoretically be designed with the use of a method called “ACH(Adler-Coppersmith-Hassner) algorithm”.

The ACH algorithm used for designing a finite-state code conversiontable will be explained herebelow. In the ACH algorithm, a number ofbits of a target code word is first taken as a parameter and a vectorcalled “approximate characteristic vector” having dimensionscorresponding to a number of states is determined based on a finitestate transition diagram of the code. Next, there is prepared a finitestates table including the same number of finite states in the finitestate transition diagram as that of elements in the approximatecharacteristic vector, and then each of operations called “statesplitting” and “state merging” is repeated to finally provide asimplified finite states table.

In the ACH algorithm, multiple approximate characteristic vectors existand the last finite states table determined varies depending upon thefirst approximate characteristic vector determined. Since there are manyoptions in each of the state splitting and state merging operations,however, using the same approximate characteristic vector will notalways result in the same last finite states table.

By appropriately assigning each code in a finite states table thusobtained to necessary information word, it is possible to provide afinite-state code conversion table. Also, all codes designed by thismethod have a finite code word constraint length and can be decodedindependently of any state. That is, it is well known that a codedesigned by the method is sliding-block decodable.

The ACH algorithm is referred in detail to the article “Algorithm forSliding Block Codes” by R. Adler, D. Coppersmith and M. Hassner, IEEETrans. on Information Theory, Vol. IT-29, No. 1, pp. 5-22, January 1983,for example.

FIG. 5 shows an 8-state finite state transition diagram premised on theNRZI modulation and which provides a (1, 7) RLL code. It should be notedhere that a state number in the finite state transition diagram shown inFIG. 5 does not corresponding to a state number in the finite-state codeconversion table.

Generally, two approximate characteristic vectors [2, 3, 3, 3, 2, 2, 2,1] and [3, 5, 5, 4, 4, 4, 3, 2] are known as 8-dimensional onesdetermined according to the finite state transition diagram in FIG. 5.The value of each element in the approximate characteristic vectorindicates a number by which each state in the finite state transitiondiagram (a so-called number of stet stripping) is first divided. Forexample, the 5-state code conversion table in FIG. 4 can be determinedaccording to the look-head code conversion tables in FIGS. 2 and 3 andalso theoretically as an approximate characteristic vector [3, 5, 5, 4,4, 4, 3, 2] using an ACH algorithm determined according to the finitestate transition diagram in FIG. 5. On the other hand, by determining afinite-state code conversion table using the ACH algorithm as theapproximate characteristic vector [2, 3, 3, 3, 2, 2, 2, 1], there can beprovided a 4-state finite-state code conversion table.

FIG. 6 shows a finite-state 4-state code conversion table of a (1, 7)RLL code by Weathers-Wolf. The code conversion table in FIG. 6 is knownas a minimum-state finite-state code conversion table of the (1, 7) RLLcode (see the article “A New Rate 2/3 Sliding Block Code for the (1, 7)Runlength Constraint with the Minimal Number of Encoder States” by A. D.Weathers and J. K. Wolf, IEEE Trans. on Info. Theory, Vol. 37, No. 3,pp. 908-913, May 1991, for example).

Generally in an optical disk recorder/player or an optical disk player,low-frequency component of a code spectrum has to be suppressed to someextent to extract a servo signal used in a low-frequency band. Since alow-frequency component of a read signal in a data area is superposed asa noise on the extracted servo signal if the low-frequency component ofthe code spectrum is not suppressed at all, the servo signal will havethe quality thereof deteriorated considerably.

The low-frequency component of a code spectrum can effectively besuppressed by controlling the DC component of a code sequence so that arunning digital sum (RDS) of the code sequence will have a digital-sumvariation (DSV) as small as possible. The “RDS” referred to herein is asum of code polarities represented by ±1 in a modulated recording codesequence or transmission code sequence, namely, in a code sequence afterNRZI-modulated in case the code sequence is based on the NRZImodulation.

Conventionally, the DC control of a code sequence is done usingprimarily the following three methods:

The first one of the methods is to encode data irrespectively of the DSVof a code sequence to be checked the RDS of the code sequence, and theninsert DC control bits at constant intervals into the code sequence sothat the DSV of the code sequence is as small as possible. On theassumption that the DC control bit is an RLL control bit as the case maybe, however, the insertion of DC control bits may be followed by a firstcoding so that the RLL limitation on the code sequence can be kept.

The codes to which the above first method is applicable include thepreviously mentioned EFM code actually used in CD and MD, for example.In the case of EFM code, however, if a certain information sequence isgiven continuously, any DC control cannot be done to keep the limitationon a (2, 10) RLL code and DSV of the code will not be finite in somecases. However, since commonly used input information has a highrandomness, the above will not be any practical problem.

The above first method is advantageous in that it is applicable to anarbitrary RLL code. However, a large number of DC control bits has to beinserted into a code sequence in order to keep the RLL limitation andthus the code redundancy including the influence of the DC control bitsis apt to be increased.

The second one of the above three methods is to pre-design a codeconversion table of a finite state type so that the DSV of a codesequence will be as small as possible. The codes to which the secondmethod is applicable include a (2, 10) RLL code called “EFMPlus” used toconvert an 8-bit information word into a 16-bit code word. This EFMPluscode is actually used as a recording code for DVD (digital versatiledisk). The aforementioned EFM code is of a fixed length. On the otherhand, the EFMPlus code has a variable length in which a plurality ofinformation words is assigned the same code word.

However, an EFMPlus code includes 256 information words, of which only95 are DC-controllable. If any ones of the other 161 information wordsare successively included in the EFMPlus code, the DSV will not befinite. Also in this case, however, input information used has a highrandomness as a rule as in the above-mentioned EFM code. Thus the abovewill not be any problem.

The second one of the aforementioned methods is advantageous in which itis not necessary to insert any DC control bit. For some codes, it isdifficult to design a code conversion table with a high coding rate. Inmany cases, the code conversion table is so complex that the encoder anddecoder are complex in construction.

The third method is to pre-assign a code word to an information word sothat two's complement of a sum of information words coincides with thatof a sum of code words and insert DC control bits at constant intervalsinto an information sequence so that the DSV of a code sequence is assmall as possible. After a code word is assigned by the third method,the inversion of a code following a DC control bit to be inserted isassured whether the DC control bit is 0 or 1. Thus, a code sequence canbe DC-controlled efficiently.

The code word assignment by the third method is called “PP (paritypreserving) word assignment” because it is done in such a manner thatthe parity of an information sequence always coincides with that of acode sequence.

More specifically, the PP word assignment worked by Kahlman and Imminkin 1994 is such that in the look-ahead code conversion table, code wordsare assigned to information words in order to meet the followingexpression (1) (see the U.S. Pat. No. 5,477,222 to J. Kahlman and A,Immink, for example):p=q  (1)where p is a complement of a sum of information words and q is acomplement of a sum of code words.

In the third method, any DC control bits inserted in an informationsequence will not disturb the RLL limitation on a code sequence. Thus,when suppressing low-frequency components of a code spectrum with anequal effect, adoption of the third method will often permit to reducethe redundancy of the DC control bits as compared with the first methodin which DC control bits are inserted in a code sequence.

In the third method, however, the inversion of a code sequence isassured through selection of DC control bits but the inversion of theRDS within a control interval is not always assured. Therefore, ifinformation pieces whose RDS polarity will not be inverted are suppliedsuccessively whether either 0 or 1 is selected as a DC control bit, theDSV will not be finite as the case may be. However, since commonly usedinput information has a high randomness similarly to the aforementionedEFM and EFMPlus codes, the above will not be any practical problem.

Also, in case the DC control method of inserting DC control bits into aninformation sequence is used, the RDS polarity of a code sequence can beinverted with a certain probability even if the PP code word assignmentis not doe in a look-ahead code conversion table used, the DC control ofthe code sequence is not quite impossible. That is, the PP code wordassignment can advantageously be used because a code sequence can besubjected to an efficient DC control by considerably increasing theprobability in inversion of the RDS of the code sequence at the time DCcontrol bits are inserted into an information sequence.

For a practical PP assignment of codes in the code conversion table,only the look-ahead code conversion table is known. Namely, for thefinite-state code conversion table determined from the ACH algorithm,there is known no PP code word assignment method, which was definitelystated by K. Immink, one of the Inventors of the PP code word assignment(see “Codes for Mass Data Storage” by K. Immink, Shannon FoundationPublishers, Netherlands, p. 290, 1999).

Also, the code represented according to the first look-ahead codeconversion table for the PP code word assignment, disclosed in the aboveU.S. Pat. No. 5,477,222, was a (1, 8) RLL code. Currently, it is knownthat a look-ahead code conversion table for the PP code word assignmentcan be designed for the (1, 7) RLL code as well.

FIGS. 7 and 8 show look-ahead code conversion tables for the PP codeword assignment of the (1, 7) RLL code.

FIG. 7 shows a basic data conversion table for use to encode aninformation sequence in normal times, and FIG. 8 shows an irregular codeconversion table for use to encode an information sequence at a fault.When an information sequence is encoded according to the basic codeconversion table in FIG. 7, it results in a (1, 8) RLL code. Coding the(1, 8) RLL code according to the irregular code conversion table in FIG.8 results in a (1, 7) RLL code. In other words, in case an informationsequence as in the irregular code conversion table is supplied forcoding, the irregular code conversion table in FIG. 8 is used for the(1, 7) RLL code preferentially over the basic code conversion table inFIG. 7. In any of the basic code conversion table in FIG. 7 andirregular code conversion table in FIG. 8, the two's complement of a sumof information words completely coincides with that of a sum of codewords (see the Japanese Published Unexamined Patent Application No.1999-346154, for example).

As described in the above Japanese Published Unexamined PatentApplication No. 1999-346154, a long sequence of minimum runs adverselyaffects the bit error rate when a defocusing, tangential tilt or thelike has occurred in the optical disk recorder/player or optical diskplayer. On this account, it has been proposed to limit the maximumnumber of minimum runs in sequence to six (6) by adding the irregularcode conversion table to the look-ahead code conversion tables in FIGS.7 and 8. It should be noted here that in a code sequence “001(01)r00”,r≦R where (01)r is a representation of (01) repeated r times insuccession and R is a maximum number of minimum runs are repeated Rtimes in succession on the assumption that the minimum run is “1” andthe modulation method is the NRZI modulation, for example.

FIG. 9 shows a look-ahead irregular code conversion table to which thePP code word assignment is applied. This look-ahead irregular codeconversion table is added to the basic code conversion table andirregular code conversion table in FIGS. 7 and 8 to limit the maximumnumber of minimum runs in sequence of a (1, 7) RLL code to six (6).

Also in the irregular code conversion table in FIG. 9, the two'scomplement of a sum of information words coincides with that of a sum ofcode words. By encoding information under the coding rule adopted in thecode conversion tables in FIGS. 7 and 8 and also that in the irregularcode conversion table in FIG. 9, it is possible to limit the maximumnumber of minimum runs in sequence to six (6) with the PP code wordassignment being maintained.

The (1, 7) RLL code represented according to the look-ahead codeconversion tables shown in FIGS. 7, 8 and 9 and to which the PP codeword assignment is applied is adopted in the recording code for theBlu-ray which is the next-generation optical disk recorder/player.

As above, the PP (parity preserving) code word assignment is one of theexcellent techniques for efficient DC control of a code sequence. Moreprecisely, the PP code word assignment has to be done according tolook-ahead code conversion tables and designed by a heuristic approach.For this reason, there have been known very few code conversion tablesactually using the PP code word assignment.

On the other hand, the finite-state code conversion table cantheoretically be designed using the ACH algorithm. Therefore, if a codeword assignment method effective similarly to the PP code wordassignment used in the look-ahead code conversion table can be found, itis possible to theoretically design a code conversion table superb in DCcontrol efficiency.

Also, techniques for conversion of a look-ahead code conversion tableinto a finite-state code conversion table have been disclosed forconversion of variable-length codes, but there has been disclosed notechnique for conversion of a finite-state code conversion table into alook-ahead code conversion table. Namely, no concrete ways of suchconversions are yet known. If a finite-state code conversion table canbe convened into a look-ahead code conversion table, it will be possibleto easily make clear the differences between the code word assignment inthe aforementioned finite-state code conversion table and theconventional PP code word assignment.

For encoding information under the coding rule in a look-ahead codeconversion table in which the PP code word assignment having beendisclosed heretofore is used, the construction of the aforementionedencoder 11 will be more complicated than in case the conventional codingmethod is used in the look-ahead code conversion table.

For example, in the look-ahead code conversion tables in FIGS. 7 and 8,the necessary looked-ahead amount of an information sequence is 3blocks. So, when a code word delayed 3 blocks is converted into afinite-state code conversion table via re-assignment to an informationword, it will have 104 states. In the encoder 11, the coding rule of thefinite-state code conversion table should not always be checked.However, since the large number of states as a result of the conversionto the finite-state code conversion table means the coding rule of thelook-ahead code conversion table is complex, the construction of theencoder 11 will be complicated as a rule.

Especially when the maximum number of minimum runs in sequence islimited finitely, the encoder 11 will be constructed to be verycomplicated. For example, in case the look-ahead code conversion tablein FIG. 9 is combined with the look-ahead code conversion tables havingbeen described above with reference to FIGS. 7 and 8, the necessarylooked-ahead amount of an information sequence is 5 blocks. So, when theinformation sequence is converted into a finite-state code conversiontable via re-assignment of a code word delayed 5 blocks to aninformation word, it will have 1691 states. This number of states isvery large.

Further, in case information is encoded according to a look-ahead codeconversion table using the PP code word assignment technique having beenproposed so face, the decoded code word constraint length will be largerthan a decoded code word length resulted from a coding done according tothe code conversion tables in FIGS. 2 and 3 and code conversion table inFIG. 6, for example. It should be noted here that the “decoded code wordconstraint length” is a number of blocks in a necessary code word thathas to be held for sliding-block decoding.

As the decoded code word constraint length is larger, the decoder 16 isnot only constructed to be more complex but the decoded errorpropagation length is larger and bit error rate after the decoding isworse. It should be noted here that the “decoded error propagationlength” is a maximum number of bits whose one-bit error will possibly bepropagated from a code sequence to an information sequence. Even in casethe maximum number of minimum runs in sequence is limited finitely, theabove problem will similarly occur.

FIG. 10 shows results of calculation of the number of code states at thetime of coding, code word constraint length at the time of decoding anddecoded error propagation length at the time of decoding in case the (1,7) RLL code having been described with reference to FIGS. 2 to 9 isused. It should be noted however that in FIG. 10, the numbers of statesin a combination of the code conversion tables in FIGS. 7 and 8 and acombination of the code conversion tables in FIGS. 7, 8 and 9,respectively, are those resulted from conversion of these look-aheadcode conversion tables into a finite-state code conversion table withthe aforementioned technique.

As will be seen in FIG. 10, the (1, 7) RLL code encoded under the codingrule in the combination of the code conversion tables in FIGS. 7 and 8or that of the code conversion tables in FIGS. 7, 8 and 9, has 104 or1691 code states at the time of coding, which is more than 20 timeslarger than the five states having been described with reference to thecode conversion tables in FIGS. 2 and 3 or the code conversion table inFIG. 4 and than the four states having been described with reference tothe code conversion table in FIG. 6. Also, as will be seen, the (1, 7)RLL code encoded under the coding rule in the combination of the codeconversion tables in FIGS. 7 and 8 or that of the code conversion tablesin FIGS. 7, 8 and 9, each using the PP code word assignment, has adecoded code word constraint length and decoded error propagation lengthabout 2 times larger than those the (1, 7) RLL code encoded according tothe code conversion tables in FIGS. 2 and 3, that in FIG. 4 or that inFIG. 6, and all the (1, 7) RLL codes thus encoded are considerablydeteriorated.

That is, a code represented according to the look-ahead code conversiontable using the already proposed PP code word assignment is more largelydeteriorated in number of code states at the time of coding, code wordconstraint length at the time of decoding and error rate propagationlength at the time of decoding than a code in which no PP code wordassignment is effected. It has been demanded to improve these values.

Also, if the maximum number of minimum runs in sequence can be reduced,it is possible to effectively improve the bit error rate even if adefocusing, tangential tilt or the like occurs in an optical disk(recorder) player. However, the maximum number of minimum runs insequence of the (1, 7) RLL code, that could be attained, is six. Therehas not been disclosed any technique for making the maximum number ofminimum runs in sequence of the (1, 7) RLL code smaller than six.

OBJECT AND SUMMARY OF THE INVENTION

It is therefore an object of the present invention to overcome theabove-mentioned drawbacks of the related art by providing a codingmethod of converting an m-bit information word continuously into ann-bit word by inserting, into an information sequence, DC control bitsfor DC control of a code sequence in which the maximum number of minimumruns in sequence of the (1, 7) RLL code can be made smaller than theconventional one (six) by making the number of code states at the timeof coding smaller than ever and the code word constraint length at thetime of decoding and error propagation length at the time of decodingsmaller than ever.

The above object can be attained by providing an encoder includingaccording to the present invention:

-   -   an information sequence generating means for generating a first        information sequence by inserting first DC control bits into an        input information sequence at predetermined intervals and a        second information sequence by inserting second DC control bits        different from the first DC control bits into the input        information sequence at the predetermined intervals;    -   a first code converting means for generating a first provisional        code sequence by making a code conversion of the first        information sequence generated by the information sequence        generating means at a conversion ratio of an information word        length m to an code word length n;    -   a second code convening means for generating a second        provisional code sequence by making a code conversion of the        second information sequence generated by the information        sequence generating means at the conversion ratio of the        information word length m to the code word length n; and    -   a selecting means for selecting either the first provisional        code sequence generated by the first code converting means or        the second provisional code sequence generated by the second        code converting means,    -   the first and second code converting means using a coding rule        by which, in case the coding rule is represented by a        finite-state code conversion table, code words are assigned to        information words so that the two's complement of a sum of        coding bits included in the first provisional code sequence is        always different from that of a sum of coding bits included in        the second provisional code sequence when a first code state of        the first provisional code sequence encoded starting with a        predetermined original state, is identical to a second code        state of the second provisional code sequence encoded starting        with the predetermined original state.

In the above encoder, the first and second cove converting means may bedesigned to make a code conversion with an information word length m of2 bits and in code conversion units of 2 bits.

Also in the above encoder, the first and second code converting meansmay use a coding rule by which the code words are assigned to theinformation words so that when the first code state is identical to thesecond code state, the two's complement of the sum of coding bitsincluded in the first provisional code sequence is always different fromthat of the sum of coding bits included in the second provisional codesequence whether the first and second DC control bits are inserted atthe first or second bit of the code conversion unit by the informationsequence generating means.

Also in the above encoder, the first and second code converting meansmay use a coding rule by which the code words are assigned to theinformation words so that when the first code state is identical to thesecond code state, the two's complement of the sum of coding bitsincluded in the first provisional code sequence is always different fromthat of the sum of coding bits included in the second provisional codesequence when the first and second DC control bits are inserted at thefirst bit of the code conversion unit by the information sequencegenerating means.

Also in the above encoder, the first and second code converting meansmay use a coding rule by which the code words are assigned to theinformation words so that when the first code state is identical to thesecond code state, the two's complement of the sum of coding bitsincluded in the first provisional code sequence is always different fromthat of the sum of coding bits included in the second provisional codesequence when the first and second DC control bits are inserted at thesecond bit of the code conversion unit by the information sequencegenerating means.

Also in the above encoder, the first and second code converting meansmay be designed to encode information with an information word length mof one block and in units of one block, and the first and second codeconverting means using a coding rule by which, in case the coding ruleis represented by a look-ahead code conversion table, code words areassigned to information words so that the two's complement of a sum ofcoding bits included in an information sequence is different from thatof a sum of coding bits included in a provisional code sequence when thenumber of blocks is odd while the two's complement of a sum of codingbits included in an information sequence coincides with that of a sum ofcoding bits included in a provisional code sequence when the number ofblocks is even.

Also in the above encoder, the first and second code converting meansmay be designed to make a code conversion with an information wordlength of 2 bits taken as one block and in units of one block under acoding rule in which the information word has a length m of 2 bits, codeword has a length n of 3 bits and the maximum run is limited to 7.

Also in the above encoder, the first and second code converting meansmay use a coding rule in which, in case the coding rule is representedby a finite-state code conversion table, the number of states is seven.

Also in the above encoder, the first and second code converting meansmay be designed to make a code conversion so that the decoded code wordconstraint length is 3 blocks.

Also in the above encoder, the first and second code converting meansmay use a coding rule in which the minimum run is limited to one,maximum run is limited to seven and the maximum number of minimum runsin sequence of code words is five and, in case the coding rule isrepresented by a code conversion table, the number of states is eight.

Also the above encoder may further comprise a code select signalgenerating means for calculating the DSV of the first provisional codesequence and that of the second provisional code sequence and generatinga code select signal indicative of the provisional code sequence whoseDSV is smaller, and the selecting means selects the provisional codesequence whose DSV is smaller according to the code select signal.

Also the above object can be attained by providing a coding methodincluding, according to the present invention, the steps of:

-   -   generating a first information sequence by inserting first DC        control bits into an Input information sequence at predetermined        intervals and a second information sequence by inserting second        DC control bits different from the first DC control bits into        the input information sequence at the predetermined intervals;    -   generating a first provisional code sequence by making a code        conversion of the first information sequence generated in the        information sequence generating step at a conversion ratio of an        information word length m to an code word length n;    -   generating a second provisional code sequence by making a code        conversion of the second information sequence generated in the        information sequence generating step at the conversion ratio of        the information word length m to the code word length n; and    -   selecting either the first provisional code sequence generated        in the first code converting step or the second provisional code        sequence generated in the second code converting step,    -   the first and second code converting steps using a coding rule        by which, in case the coding rule is represented by a        finite-state code conversion table, code words are assigned to        information words so that the two's complement of a sum of        coding bits included in the first provisional code sequence is        always different from that of a sum of coding bits included in        the second provisional code sequence when a first code state of        the first provisional code sequence encoded starting with a        predetermined original state, is identical to a second code        state of the second provisional code sequence encoded starting        with the predetermined original state.

Also the above object can be attained by providing a recording mediumhaving recorded therein a coding program having a computer convert asequence of m-bit information words into a sequence of n-bit code words,the program including, according to the present invention, the steps of:

-   -   generating a first information sequence by inserting first DC        control bits into an input information sequence at predetermined        intervals and a second information sequence by inserting second        DC control bits different from the first DC control bits into        the input information sequence at the predetermined intervals;    -   generating a first provisional code sequence by making a code        conversion of the first information sequence generated in the        information sequence generating step at a conversion ratio of an        information word length m to an code word length n;    -   generating a second provisional code sequence by making a code        conversion of the second information sequence generated in the        information sequence generating step at the conversion ratio of        the information word length m to the code word length n; and    -   selecting either the first provisional code sequence generated        in the first code converting step or the second provisional code        sequence generated in the second code converting step,    -   the first and second code converting steps using a coding rule        by which, in case the coding rule is represented by a        finite-state code conversion table, code words are assigned to        information words so that the two's complement of a sum of        coding bits included in the first provisional code sequence is        always different from that of a sum of coding bits included in        the second provisional code sequence when a first code state of        the first provisional code sequence encoded starting with a        predetermined original state, is identical to a second code        state of the second provisional code sequence encoded starting        with the predetermined original state.

Also the above object can be attained by providing a coding program forconverting an m-bit information word into an n-bit code word, theprogram including, according to the present invention, the steps of:

-   -   generating a first information sequence by inserting first DC        control bits into an input information sequence at predetermined        intervals and a second information sequence by inserting second        DC control bits different from the first DC control bits into        the input information sequence at the predetermined intervals;    -   generating a first provisional code sequence by making a code        conversion of the first information sequence generated in the        information sequence generating step at a conversion ratio of an        information word length m to an code word length n;    -   generating a second provisional code sequence by making a code        conversion of the second information sequence generated in the        information sequence generating step at the conversion ratio of        the information word length m to the code word length n; and    -   selecting either the first provisional code sequence generated        in the first code converting step or the second provisional code        sequence generated in the second code converting step,    -   the first and second code converting steps using a coding rule        by which, in case the coding rule is represented by a        finite-state code conversion table, code words are assigned to        information words so that the two's complement of a sum of        coding bits included in the first provisional code sequence is        always different from that of a sum of coding bits included in        the second provisional code sequence when a first code state of        the first provisional code sequence encoded starting with a        predetermined original state, is identical to a second code        state of the second provisional code sequence encoded starting        with the predetermined original state.

Also the above object can be attained by providing an encoder includingaccording to the present invention:

-   -   an input means for receiving an m-bit information word;    -   a coding means for encoding the m-bit information word into an        n-bit code word under a coding rule in which the minimum run is        limited to one, maximum run is limited to seven and the maximum        number of minimum runs in sequence of decoded code words is        three to five; and    -   an output means for outputting the n-bit code words.

In the above encoder, coding means may use a coding rule in which, incase the coding rule is represented by a code conversion table, thenumber of states is eight and the maximum number of minimum runs insequence is five.

Also in the above encoder, the coding means may be designed to encodethe m-bit information words with a decoded code word constraint lengthof 4 blocks.

Also the above object can be attained by providing a coding methodincluding, according to the present invention, the steps of:

-   -   receiving an m-bit information word;    -   encoding the m-bit information word into an n-bit code word        under a coding rule in which the minimum run is limited to one,        maximum run is limited to seven and the maximum number of        minimum runs in sequence of a decoded code word is three to        five; and    -   outputting the n-bit code words.

Also the above object can be attained by providing a recording mediumhaving recorded therein a coding program, the program including,according to the present invention, the steps of:

-   -   receiving an m-bit information word;    -   encoding the m-bit information word into an n-bit code word        under a coding rule in which the minimum run is limited to one,        maximum run is limited to seven and the maximum number of        minimum runs in sequence of a decoded code word is three to        five; and    -   outputting the n-bit code words.

Also the above object can be attained by providing a coding program forconverting an m-bit information word continuously into an n-bit codeword, the program including, according to the present invention, thesteps of:

-   -   receiving an m-bit information word;    -   encoding the m-bit information word into n-bit code word under a        coding rule in which the minimum run is limited to one, maximum        run is limited to seven and the maximum number of minimum runs        in sequence of a decoded code word is three to five; and    -   outputting the n-bit code words.

These objects and other objects, features and advantages of the presentinvention will become more apparent from the following detaileddescription of the preferred embodiments of the present invention whentaken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a block diagram of the conventional recorder/player;

FIG. 2 explains the look-ahead code conversion table for the (1, 7) RLLcode;

FIG. 3 also explains the look-ahead code conversion table for the (1, 7)RLL code;

FIG. 4 explains the finite state-type 5-state code conversion tableresulted from conversion of the code conversion tables in FIGS. 2 and 3;

FIG. 5 is the 8-state transition diagram which provides the (1, 7) RLLcode;

FIG. 6 explains the finite state-type 4-state code conversion table forthe (1, 7) RLL code;

FIG. 7 explains the look-ahead code conversion table using the PP(parity preserving) code word assignment of the (1, 7) RLL code;

FIG. 8 also explains the look-ahead code conversion table using the PPcode word assignment of the (1, 7) RLL code;

FIG. 9 explains the irregular code conversion table that is to be addedto each of the code conversion tables in FIGS. 7 and 8 to limit themaximum number of minimum runs in sequence to six;

FIG. 10 explains the number of states, code word constraint length anderror propagation length of the conventional (1, 7) RLL code;

FIG. 11 is a block diagram of the recorder/player according to thepresent invention;

FIG. 12 is also a block diagram showing the construction of an encoderin FIG. 11;

FIG. 13 shows a flow of operations made during coding in the encoder inFIG. 12;

FIG. 14 explains the states of two sequences during coding made in theencoder in FIG. 12;

FIG. 15 explains a 7-state finite state table for the (1,7) RLL code;

FIG. 16 is a block diagram of a personal computer;

FIG. 17 shows a flow of operations made in detection of a codeconversion table;

FIG. 18 explains acceptable numbers of code words assignments per blocklength;

FIG. 19 explains a type classification of acceptable code wordassignment, not dependent upon any block length;

FIG. 20 explains a first acceptable example of the finite state-type7-state code conversion table of the (1, 7) RLL code;

FIG. 21 explains a second acceptable example of the finite-state-type7-state code conversion table of the (1, 7) RLL code;

FIG. 22 explains a third acceptable example of the finite state-type7-state code conversion table of the (1, 7) RLL code;

FIG. 23 explains the states of two sequences during coding made in theencoder in FIG. 12;

FIG. 24 explains an acceptable look-ahead code conversion table for the(1, 7) RLL code, resulted from conversion of the code conversion tablein FIG. 20;

FIG. 25 explains an acceptable look-ahead code conversion table for the(1, 7) RLL code, resulted from conversion of the code conversion tablein FIG. 21;

FIG. 26 explains an acceptable look-ahead code conversion table for the(1, 7) RLL code, resulted from conversion of the code conversion tablein FIG. 22;

FIG. 27 explains the dependence of the power spectral density on the DCcontrol redundancy;

FIG. 28 explains the dependence of the power spectral density on the DCcontrol redundancy;

FIG. 29 explains the maximum number of minimum runs in sequence, and theShannon capacity;

FIG. 30 is a 18-state transition diagram of the (1, 7) RLL code, inwhich the maximum number of minimum runs in sequence is limited to five;

FIG. 31 explains an 8-state finite state table for the (1, 7) RLL code,in which the maximum number of minimum runs in sequence is limited tofive;

FIG. 32 explains a number of acceptable code word assignments by typeclassification, not dependent upon any block length;

FIG. 33 explains a finite state-type 8-state code conversion table forthe (1, 7) RLL code, in which the maximum number of minimum runs insequence is limited to five;

FIG. 34 explains an irregular code conversion table that is to be addedto each of the basic code conversion table in FIG. 25 in which themaximum number of minimum runs in sequence is limited to five; and

FIG. 35 explains the number of code states at the time of coding, codeword constraint length at the time of decoding and error propagationlength at the time of decoding in the 7-state code conversion tables inFIGS. 20 to 22 and 8-state code conversion table in FIG. 33.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

The present invention will be described concerning the embodimentsthereof with reference to the accompanying drawings.

Referring now to FIG. 11, there is schematically illustrated in the formof a block diagram a recorder/player 31 according to the presentinvention. It should be noted that the elements of this recorder/player31, corresponding to those of the conventional recorder/player 1 shownin FIG. 1 are indicated with the same references as those used in FIG. 1and will not be described below wherever appropriate. As will be seen,the recorder/player 31 shown in FIG. 11 is similar in construction tothe recorder/player 1 in FIG. 1 except for a coding unit 51 provided inplace of the encoder 11.

The recorder/player 31 shown in FIG. 11 may be composed of two units,namely, an encoder 41 composed of the coding unit 51 and arecording/playback unit 12, and a decoder 42 composed of therecording/playback unit 12 (also used in the encoder 41), an analogequalizer 13, A-D (analog-to-digital) converter 14, code detector 15 anda decoder 16. It should be noted that the decoder 42 may be designed toacquire a code sequence encoded by the encoder 41 and transmitted over anetwork (not shown) and decode the code sequence.

In the recorder/player 31 or decoder 42 shown in FIG. 11, a digitalequalizer may additionally be provided between the A-D converter 14 andcode detector 15 as in the conventional recorder/player 1 in FIG. 1 incase the code sequence cannot be equalized satisfactorily by the analogequalizer 13. It should be noted that in this case, a lowpass filler maybe provided in place of the analog equalizer 13.

The coding unit 51 in FIG. 11 makes a DC control of a code sequence viaa coding of the code sequence by inserting DC control bits into aninformation sequence as will be described below:

FIG. 12 schematically shows, in the form of a block diagram, theconstruction of the coding unit 51 shown in FIG. 11 and which makes a DCcontrol of a code sequence by inserting DC control bits into aninformation sequence as will be described herebelow.

The coding unit 51 includes a DC control bit inserting unit 101 that iscontinuously supplied with an information sequence in units of a byte (8bits). The DC control bit inserting unit 101 generates an informationsequence do having provisional DC control bits 0 inserted therein atpredetermined DC control intervals T_(dc) and an information sequence d₁having provisional DC control bits 1 inserted therein at thepredetermined DC control intervals T_(dc), and supplies the informationsequence d₀ to an m-n converter 102 also included in the coding unit 51and the information sequence d₁ to an m-n converter 103 also included inthe coding unit 51.

In case the DC control bits are inserted into the information sequencesupplied to the DC control bit inserting unit 101 at the intervalsT_(dc), the DC control bit inserting unit 101 provides an outputsequence having a DC control redundancy of 1/(T_(dc)+1) in relation tothe input sequence.

The DC control bit inserting unit 101 also supplies a DC control signalindicative of a DC control time to the m-n converter 102, m-n converter103 and to a code select signal generator 106 also included in thecoding unit 51.

The m-n converter 102 converts the supplied information sequence d₀ intoa provisional code sequence c₀ at a conversion ratio of m to n, andsupplies the provisional code sequence c₀ to a delay unit 104 alsoincluded in the coding unit 51 and to the code select signal generator106 in units of n bits. Similarly, the m-n converter 103 converts thesupplied information sequence d₁ into a provisional code sequence c₁ atthe conversion ratio of m to n, and supplies the provisional codesequence c₁ to a delay unit 105 also included in the coding unit 51 andto the code select signal generator 106 in units of n bits.

The delay unit 104 delays the supplied provisional sequence c₀ by the DCcontrol interval and supplies it to a code selector 107 also included inthe coding unit 51. Similarly, the delay unit 105 delays the suppliedprovisional sequence c₁ by the DC control interval and supplies it tothe code selector 107.

The code select signal generator 106 calculates RDS of each of thesupplied provisional code sequences c₀ and c₁, then generates a codeselect signal indicative of which the code to be selected is, theprovisional code sequence c₀ or c₁, to reduce the code sequence DSV asfar as possible, and outputs it the m-n converts 102 and 103 and to thecode selector 107 correspondingly to the supply timing of the DC controlsignal.

The code selector 107 is supplied with the delayed provisional codesequences c₀ and c₁, selects, based on the code select signal suppliedfrom the code select signal generator 106, any one of the provisionalcode sequences that can have the DSV reduced as far as possible, andoutputs it as a code sequence.

Note here that each of the m-n converters 102 and 103 incorporates aninternal register for holding a code state at each time and copies,based on the supplied DC control signal and code select signal, the codestate in the m-n converter 102 into the internal register of the m-nconverter 103 when the provisional code sequence c₀ has been selected,and the code state in the m-n converter 103 into the internal registerof the m-n converter 102 when the provisional code sequence c₁ has beenselected.

The coding unit 51 make coding operations as will be described belowwith reference to the flow chart in FIG. 13. It should be assumed herethat the coding unit 51 is capable of making a DC control of the codesequence by receiving an input information sequence of N_(i) bytes andinserting DC control bits into the input information sequence atintervals of T_(dc) bits.

In step S1, the DC control bit inserting unit 101 initializes variablesi and j to zero (0), the m-n converter 102 assigns an initial state s₁to the state s₀ of the internal register, and also the m-n converter 103assigns the initial state si to the state s₁ of the internal register.It should be noted here that the variable i indicates the number ofprocessed bytes and variable j counts bits for inserting the DC controlbits at correct intervals.

The DC control bit inserting unit 101 acquires 1-byte informationsequence in step S2, and sets the variable i to i+1 and variable j toj+8 in step S3.

In step S4, the DC control bit inserting unit 101 judges whether thevariable j satisfies a condition that j<T_(dc).

In case it is determined in step S4 that the variable j does not thesatisfy the condition that j<T_(dc), the coding unit 51 goes to step S5where the DC control bit inserting unit 101 will insert DC control bits0 into the supplied information sequence to generate an informationsequence d₀, and supply the information sequence d₀ to the m-n converter102, while inserting DC control bits 1 into the supplied informationsequence to generate an information sequence d₁ and supplying theinformation sequence d₁ to the m-n converter 103, and then set thevariable j to j−T_(dc).

If it is determined in step S4 that the variable j satisfies thecondition that j<T_(dc), the coding unit 51 goes to step S5. Aftercompletion of step S5, the coding unit 51 goes to step S6 where the m-nconverters 102 and 103 will encode the information sequences d₀ and d₁supplied to them, respectively, at a coding ratio of m/n to generateprovisional code sequences c₀ and c₁, respectively. The m-n converter102 outputs the provisional code sequence c₀ to the code select signalgenerator 106 and delay unit 104, while the m-n converter 103 outputsthe provisional code sequence c₁ to the code select signal generator 106and delay unit 105.

In step S7, the code select signal generator 106 calculates DSV of eachof the supplied provisional code sequences c₀ and c₁ to provide DSV0 forthe provisional code sequence c₀ and DSV1 for the provisional codesequence c₁.

In step S8, the code select signal generator 106 compares thecalculation results (DSV0 and DSV1) in step S7 to judge whetherDSV0>DSV1.

In case it is determined in step S8 that DSV0 is not larger than DSV1,the code select signal generator 106 supplies the m-n converters 102 and103 and code selector 107 with a code select signal for selection of theprovisional code C₀ as an output code sequence. Thus, in step S9, thecode selector 107 will take an output code sequence c₂ as c₀ and the m-nconverter 103 will replace the state s₁ of the internal register thereofwith the state s₀ of the internal register of the m-n converter 102.

In case it is determined in step S8 that DSV0>DSV1, the code selectsignal generator 106 supplies the m-n converters 102 and 103 and codeselector 107 with a code select signal for selection of the provisionalcode c₁ as an output code sequence. Thus, in step S10, the code selector107 will take an output code sequence c₂ as c₁ and the m-n converter 102will replace the state s₀ of the internal register thereof with thestate s₁ of the internal register of the m-n converter 103.

In step S11, the code selector 107 outputs the code sequence C₂.

In step S12, the DC control bit inserting unit 101 compares the variablei with a number N₁ of supplied bytes to judge whether the variable isatisfies a condition that i<N₁. If it is determined in step S12 thatthe variable i satisfies the condition that i<N₁, the coding unit 51returns to step S2 where it will repeat the operations in step S2 andsubsequent steps. In case it is determined in step S12 that the variablei does not satisfy the condition that i<N₁, the coding unit 51 exits thecoding procedure.

With the above operations, there are generated the encoded provisionalcode sequence c₀ having provisional DC control bits 0 inserted thereinat an interval of T_(dc) bits and the encoded provisional code sequencec₁ having a provisional DC control bit 1 inserted therein at theinterval of T_(dc) bits, and any of the provisional code sequences isselected based on the result of DSV calculation, and provided as thecode sequence c₂. Thus, the code sequence can undergo the DC control.

As aforementioned, only the look-ahead code conversion table using thePP code word assignment is known as the code conversion table used inthe coding procedure in step S6 in FIG. 13, and it can only be designedby a heuristic approach. If a code word assignment method having thesame effect at the PP code word assignment method is available for usein the finite-state code conversion table, however, it is possible todesign a theoretic conversion table using the ACH algorithm and therecan thus be provided codes more excellent than the conventional ones.

Next, there will be explained a characteristic required for a codeconversion table permitting an efficient DC control of a code sequencein case an information sequence is encoded according to a coding rule ofthe finite-state code conversion table by inserting DC control bits intothe information sequence at predetermined bit intervals as in the codingunit 51 having been described above with reference to FIG. 12.

As having been described with reference to FIGS. 12 and 13, in case aninformation sequence having a provisional DC control bit 0 inserted in aspecific position such as the top thereof is taken as an informationsequence d₀ and an information sequence having a provisional DC controlbit 1 inserted at the top thereof is taken as an information sequenced₁, for example, provisional code sequences resulted from encoding ofthe two information sequences d₀ and d₁ starting with the same stateunder the coding rule of the finite-state code conversion table areprovisional code sequences c₀ and c₁, respectively. In this case, thecode states at the time of the coding, stored in the internal registersof the m-n converters 102 and 103, respectively, are states s₀ and s₁,respectively.

For example, in case coding is done according to the code conversiontable having been explained with reference to FIG. 6, when 7 bits “1, 1,0, 0, 0, 1, 0” is supplied as an information sequence, the informationsequences d₀ and d₁ having the provisional DC control bits inserted atthe tops thereof, respectively, provisional code sequences c₀ and c₁resulted from coding of these information sequences d₀ and d₁ startingwith a state 2 according to the code conversion table in FIG. 6, andcode states s₀ and s₁ at the time of coding will be d₀01, 10, 00, 10,c₀: 100, 101, 000, 010 and s₀: 2, 3, 1, 3, and d₁: 11, 10, 00, 10, c₁:101, 010, 000, 010 and s₁: 4, 3, 1, 3, as shown in FIG. 14.

In the coding shown in FIG. 14, the states s₀ and s₁ of the provisionalcode sequences differ from each other since the corresponding inputinformation words are different by 1 bit from each other even if theprovisional code sequences are identical in initial state to each other.Thus, the state s₀=2 while the state s₁=4. Thereafter, however, thestates will be s₀=s₁=3 in the second block. Once the states s₀ and s₁are thus identical to each other, the provisional code sequences in thethird and subsequent blocks will be identical to each other and thestates thereof be identical to each other.

As above, the provisional code sequence c₀ resulted from coding ofinformation sequence d₀ resulted from insertion of a provisional DCcontrol bit 0 into an arbitrary information sequence, and theprovisional code sequence c₁ resulted from coding of the informationsequence d₁ resulted from insertion of a provisional DC control bit 1into the arbitrary information sequence, will initially identical toeach other and the initial states s₀ and s₁ thereof initially beidentical to each other but will differ from each other once in manycases since the first input information words (that is, the provisionalDC control bits) having been inserted into the original arbitraryinformation sequence are different by 1 bit from each other. Once thestates s₀ and s₁ are made identical to each other by any subsequentconversion, however, the two provisional code sequences and their stateswill be identical to each other whatever the subsequent informationsequence is.

Therefore, if the polarities of the provisional code sequences c₀ and c₁after subjected to the NRZI modulation have been inverted when thestates s₀ and s₁ become identical to each other, the RDS polarities ofthe subsequent provisional code sequences c₀ and c₁ will be invertedwithout fail. Thus, by selecting either of the provisional codesequences c₀ and c₁ as a fine code sequence so that the code sequenceswill have a DSV as small as possible, it is possible to attain anefficient DC control of the code-sequences.

To invert the polarities of the provisional code sequences c₀ and c₁after subjected to the NRZI modulation when the states s₀ and s₁ of theprovisional code sequences c₀ and c₁ become identical to each other, theparity q₀ as the two's complement of a sum of the provisional codesequences c₀ and the parity q₁ as the two's complement of a sum of theprovisional code sequences c₁, after the code sequences become identicalin state to each other, should be different in value from each other.

More specifically, for efficient DC control of code sequences byinserting DC control bits into an information sequence at constantintervals in encoding the information sequence according to thefinite-state code conversion table, the following expression (2) shouldalways be met by the parity q₀ of the provisional code sequence c₀resulted from a provisional encoding, starting with an arbitrarystart-point state, of an information sequence having a first insertionbit inserted therein and the parity q₁ of the provisional code sequencec₁ resulted from encoding, starting with the same start-point state, ofthe information sequence having a second insertion bit inserted thereinwhen the states s₀ and s₁ become identical to each other:q ₀ ≠q ₁  (2)

After the states s₀ and s₁ becomes identical to each other, theprovisional code sequences c₀ and c₁ are identical to each other. So, ifthe expression (2) holds when the states s₀ and s₁ become identical toeach other, the parities q₀ and q₁ of the provisional code sequencesafter the states s₀ and s₁ become identical to each other meet conditiongiven by the expression (2).

In the coding shown in FIG. 14, the two's complement q₀ of the sum ofthe code sequences c₀ “1, 0, 0, 1, 0, 1” up to the second block in whichthe states s₀ and s₁ become identical to each other is 1 and also thetwo's complement q₁ of the sum of the code sequences c₁ “1, 0, 1, 0, 1,0” up to the second block is 1. In this case, the expression (2) doesnot hold. That is, in case the DC control bit is inserted at the firstbit of the information word, the expression (2) will not hold for anyarbitrary information sequence as will be known from the code conversiontable in FIG. 6.

Also, it will be known from the code conversion table in FIG. 6, theexpression (2) will not hold for any information sequence even in casethe DC control bit is inserted at the second bit of the informationword.

It is explained here that the expression (2) does not hold for a singleinformation sequence. However, if the expression (2) holds for aninformation sequence, it is necessary to check if the expression (2)holds for other arbitrary information sequences.

More particularly, there are determined two's complements q₀ and q₁ ofsums of provisional code sequences c₀ and c₁, respectively, resultedfrom encoding, starting with a fixed start-point state, of aninformation sequence d₀ having a block length L in which the bit in aspecific position (top bit, for example) is 0 and an informationsequence d₁ having the block length L in which the bit in the specificposition is 1, respectively, until the states of the provisional codesequences become identical to each other for the first time. Then, it ischecked concerning all possible information sequences having the blocklength L and all start-point states whether the two's complements q₀ andq₁ are different from each other.

However, in case the states become identical to each other in a blockshorter than the length L, the information sequences are identical toeach other until the states are identical to each other. In this case,it is not necessary to check whether the expression (2) holds for anyinformation sequences having a block length smaller than the length L.Since the information sequence has an arbitrary length, it is impossibleto make infinite the block length L in which the information sequencesare to be checked. Thus, the length L should be a finite one. Further,if the states does not become identical to each other within the blocklength L in which the information sequences are to be checked, theinformation sequences should be disregarded.

Note here that it will be described later with reference to FIG. 18whether the expression (2) holds also for an arbitrary informationsequence having an infinite block length in a code conversion table ifthe expression (2) holds for an arbitrary information sequence having afinite block length L in the code conversion table.

It was verified whether there existed a code word assignment meetingcondition given by the expression (2) for an arbitrary informationsequence in case the code word assignment to each information word waschanged in the 4-state code conversion table in FIG. 6, for example. Theresult of verification showed that when the length L of an informationsequence including DC control bits is more than 4 blocks, none of(4!)4=331.776 code word assignments met condition given by theexpression (2) for any arbitrary information sequence in the 4-statecode conversion table in FIG. 6 whether the DC control bit was insertedat the first or second bit.

Similarly, it was verified whether there existed a code word assignmentmeeting condition given by the expression (2) for an arbitraryinformation sequence in case the code word assignment to eachinformation word was changed in the 5-state code conversion table inFIG. 4, for example. The result of verification showed that when thelength L of an information sequence including DC control bits is morethan 5 blocks, none of (4!)5=7,962,624 code word assignments metcondition given by the expression (2) for any arbitrary informationsequence in the 5-state code conversion table in FIG. 4 whether the DCcontrol bit was inserted at the first or second bit.

As above, in the conventional 4- or 5-state finite state (1, 7) RLL codeconversion table, there existed no code word assignment that metcondition given by the expression (2) for any arbitrary informationsequence even when the code word assignment was altered.

On the other hand, condition given by the expression (2) was satisfiedfor an arbitrary information sequence in a 104-state finite state codeconversion table resulted from re-assignment of a 3 bit code word to a2-bit information word in each of the look-ahead code conversion tablesin FIGS. 7 and 8 by delaying the 3-bit code word by 3 blocks and a1691-state finite state code conversion table resulted fromre-assignment of a 3-bit code word to a 2-bit information word in eachof the look-ahead code conversion tables in FIGS. 7, 8 and 9 by delayingthe 3-bit code word by 5 blocks. However, making the number of statessmaller than that of codes subjected to the PP code word assignment isextremely difficult unless a finite-state code conversion table whosenumber of states is as small as possible is designed and then a codeword assignment meeting condition given by the expression (2) for anarbitrary information sequence.

On this account, the present invention proposes to provide a code wordassignment meeting condition given by the expression (2) for anarbitrary information sequence in a finite-state code conversion tablewhose number of states is relatively small by designing a newfinite-state table using the ACH algorithm based on an “approximatecharacteristic vector” different from the conventional approximatecharacteristic vector.

More specifically, an approximate characteristic vector “4, 6, 6, 6, 4,4, 4, 2” was derived as an 8-dimensional approximate characteristicvector that can be determined from the finite-state transition diagramin FIG. 5. The conventional approximate characteristic vector as the ACHalgorithm is “2, 3, 3, 3, 2, 2, 2, 1”. As will be known, each element ofthis new approximate characteristic vector is a double of each elementof the conventional approximate characteristic vector. A 7-state finitestate table was newly determined using the ACH algorithm on the basis ofthe new approximate characteristic vector.

FIG. 15 shows a 7-state finite state table for the (1,7) RLL limitation,determined using the ACH algorithm on the basis of the approximatecharacteristic vector “4, 6, 6, 6, 4, 4, 4, 2”. In the 7-state finitestate table in FIG. 15, no code word assignment has yet been done to aninformation word. To provide a code conversion table on the basis of thefinite state table in FIG. 15, a 3-bit code word of each state has to beassigned to a 2-bit information word in 4 kinds: 00, 01, 10 and 11. Suchan code word assignment in the finite state table in FIG. 15 is in(4!)7=4,586,471,424 kinds.

Next, there will be described how to judge whether a code wordassignment meeting condition given by the expression (2) for anarbitrary information sequence exists in the finite state table in FIG.15 when a code word assignment has been done to an information word.

A finite state table can be searched by a personal computer as shown inFIG. 16 or the like, not depending upon any block length L to bechecked, for a code word assignment meeting condition given by theexpression (2) for an arbitrary information sequence.

FIG. 16 shown an example of the construction of a personal computer. Asshown, the personal computer, generally indicated with a reference 121,includes a CPU (central processing unit) 131 that makes variousoperations according a program stored in a ROM (read-only memory) 132 ora program loaded to a RAM (random-access memory) 133 from a hard disk(HDD) 138. The RAM 133 appropriately stores necessary data for the CPU131 to execute various operations.

The CPU 131, ROM 132 and RAM 133 are connected to each other via aninternal bus 134. The internal bus 134 has also an input/outputinterface 135 connected thereto.

The input/output interface 135 has connected thereto an input unit 137consisting of a keyboard, mouse and the like, and output unit 136consisting of a display such as a CRT (cathode ray tube), LCD (liquidcrystal display), or the like and that displays an image and text and aspeaker that outputs a sound, an HDD 138 that records and reproducesinformation, and a network interface 140 consisting of a modem, terminaladapter and the like. The network interface 140 makes communications viaa network such as Internet, for example.

The input/output interface 135 has also a drive 139 connected thereto asnecessary. The drive 139 has connected thereto a magnetic disk drive141, optical disk drive 142, magneto-optical disk drive 143,semiconductor memory 144 or the like appropriately, and a computerprogram read from any of these units is installed into the HDD 138 asnecessary.

As will be described below with reference to the flow chart in FIG. 17,a finite state table is searched by the personal computer 121 as shownin FIG. 16 or the like, not depending upon any block length L to bechecked, for a code word assignment meeting condition given by theexpression (2) for an arbitrary information sequence.

In step S31, based on a user's command supplied from the input unit 137or information pre-stored in the HDD 138, the CPU 131 acquires a finitestate table to be checked using the ACH algorithm, for example. Forexample, the CPU 131 determines the 8 dimensional approximate charactervector “4, 6, 6, 6, 4, 4, 4, 2” from the finite-state transition diagramin FIG. 5, and the 7-state finite table shown in FIG. 15 and thatprovides a (1, 7) RLL limitation using the ACH algorithm.

In step S32, the CPU 131 reads variables L and N₀ provisionally storedin the RAM 133, initializes them by assigning zeros (0) to them, andthen stores the initialized variables into the RAM 133 again. It shouldbe noted here that the variable L is a block length to be checked andvariable N₀ is a number of code word assignments meeting condition givenby the expression (2) for an arbitrary information sequence having thevariable L that indicates the block length.

In step S33, the CPU 131 increments the value of the variable Lprovisionally stored in the RAM 133 by one (1) to set L to L+1, sets avariable M to 0, assigns N₀ to an variable N₁ to set N₁ to N₀, thenassigns zero (0) to N₀, and stores the variables into the RAM 133 again.It should be noted here that the variable N₁ is the value of thepreviously calculated N₀ and the variable M is a number of code wordassignments.

In step S34, the CPU 131 increments the variable M provisionally storedin the RAM 133 to set the variable M to M+1, stores the variable M intothe RAM 133 again. Namely, it changes or updates the code wordassignment. For example, in case the finite state table in FIG. 15 isacquired in step S31, 3-bit code word is assigned to four kinds of 2-bitinformation word, namely, the code word assignment is changed orupdated, in step S34, to a new code word assignment having not ever beensearched for. However, the first code word assignment to search for maybe an arbitrary one but the second or subsequent code word assignmentsto search for should be new ones having not ever been searched for.

In step S35, the CPU 131 judges whether there exists any one informationsequence whose block length is L, in which condition given by theexpression (2) is not met, namely, q₀=q₁, when the states s₀ and s₁ inthe provisional code sequences c₀ and c₁ coincide with each other ashaving been described above with reference to FIGS. 12 to 14. In case itis determined in step S35 that there exists no information sequencewhose block length is L, in which q₀=q₁, the CPU 131 goes to step S36.If it is determined in step S35 that there exists an informationsequence whose block length is L, in which q₀=q₁, the CPU 131 goes tostep S37.

However, in case it is determined in step S35 that there is noinformation sequence for which two provisional code sequences coincidein state with each other, the CPU 131 may go to step S36 or S37. It isassumed herein that the CPU 131 will go to step S37. In this case,however, the CPU 131 operates on the assumption that in at least one ofall the code word assignments having been searched for, there exists atleast one information sequence for which two code sequences coincide instate with each other.

In case it is determined in step S35 that there exists no informationsequence whose block length is L, in which q₀=q₁, the CPU 131 goes tostep S36 where it will increment the value of the variable N₀ by one (1)to set N₀ to N₀+1 while storing a code conversion table using the codeword assignment in consideration or necessary and sufficient informationfor representation of a code conversion table using that code wordassignment into the RAM 133.

In step S37, the CPU 131 reads and compares the variable M and totalnumber M_(p) of code word assignments provisionally stored in the RAM133 to judge whether M<M_(p). The total number M_(p) of code wordassignments is (4!)7=4,586,471,424 in the case of the finite state tablehaving been described with reference to FIG. 15, for example. If it isdetermined in step S37 that M is smaller than M_(p), the CPU 131 returnsto step S34 where it will repeat the above operations.

If it is determined in step S37 that M is not smaller than M_(p), theCPU 131 goes to step S38 where it will read the variables N₁ and N₀provisionally stored in the RAM 133 and judge whether N₀≠N₁ and N₀≠0. Ifit is determined in step S38 that N₀≠N₁ and N₀≠0, the CPU 131 returns tostep S33 where it will repeat the above operations. In case it isdetermined in step S38 that the conditions N₀≠N₁ and N₀≠0 are not met,the CPU 131 exists the code conversion table searching procedure.

The code conversion table stored after the last L-dependent searchthrough the code conversion table searching procedure having beendescribed with respect to FIG. 17 includes all code word assignmentsmeeting condition given by the expression (2) for an arbitraryinformation sequence, not dependent upon the block length L to bechecked, and the variable N₀ indicates the number of such code wordassignments. That is, when N₀=0, there exists no code word assignmentmeeting condition given by the expression (2) for an arbitraryinformation sequence in the finite state table.

Next, a number N(L) of code word assignments meeting condition given bythe expression (2) for an arbitrary information sequence was determinedas in the flow chart in FIG. 17 in case the block length L of aninformation sequence including DC control bits is changed for all the(4!)7=4,586,471,424 code word assignments in the 7-state finite table inFIG. 15.

However, since the finite state table in FIG. 15 is prepared using theACH algorithm, a code resulted from a coding according to the finitestate table having subjected to any code word assignment in the finitestate table in FIG. 15 can be decoded by the “sliding block”, but thecode word constraint lengths at the time of decoding include a 4-blockone and a 3-block one. The code word assignments for the code wordconstraint length at the time of decoding to be 3 blocks count382,205,952 which is equivalent to 1/12 of the total number.

FIG. 18 shows acceptable numbers N(L) of code word assignments meetingcondition given by the expression (2) for an arbitrary informationsequence whose block length is L when the block length L to be checkedis changed in the finite state table in FIG. 15. There are shown thenumbers of code word assignments which are when the code word constraintlengths are 4 blocks and 3 blocks, respectively, at the time ofdecoding. Also, whether a DC control bit is inserted fixedly at thefirst bit or second bit of an information word, calculation results inthe same number N(L) of code word assignments meeting condition given bythe expression (2).

More specifically, in the case of the constraint length 4, 955,514,880code word assignments meet condition given by the expression (2) whenthe block length L is one. As the number of blocks increases, the numberN(L) of word code word assignments meeting condition given by theexpression (2) decreases. When the block length L is six, such code wordassignments count 327,680. Even when the block length L is seven, thenumber N(L) of code word assignments is 327,680 which is the same aswhen the block length L is six.

On the other hand, in the case of the constraint length 3, 63,700,992code word assignments meet condition given by the expression (2) whenthe block length L is one, and 68,950,144 code word assignments meetthat expression (2) when the block length L is two. As the number ofblocks increases, the number N(L) of the code word assignments meetingcondition given by the expression (2) decreases and counts 65,536 whenthe block length L is six. Even when the block length L is seven, thenumber N(L) of code word assignments meeting condition given by theexpression (2) is 65,536 which is the same as when the block length L issix.

That is, as shown in FIG. 18, the number N(L) of code word assignmentsmeeting condition given by the expression (2) increases as the blocklength L, which is less than six, increases except that the block lengthL increases from one to two in the case of the constraint length 3, butit does not increase when the block length L increases from six toseven.

Also, all the 393,216 code word assignments (with the constraint lengths4 and 3) meeting condition given by the expression (2) for an arbitraryinformation sequence whose block length L is six meet that expression(2) (given by the expression (2)) for arbitrary information sequenceseven when the block length L is increased to seven or eight. Further,some extracted at random from the 393,216 code word assignments werefound to meet condition given by the expression (2) for an arbitraryinformation sequence even when the block length L was increased totwelve, for example.

The reason for the above is that when the block length L is increased tosome extent, two provisional code sequences which do not coincide incode state with each other will repeat themselves. Therefore, even ofthe block length L is infinitely great (which however is actuallyimpossible), the above 393,216 code word assignments will meet conditiongiven by the expression (2).

That is, a number N(L) of the code word assignments, found when thefollowing expression (3) holds as a result of calculating a number N(L)of code word assignments meeting condition given by the expression (2)as the block length L to be checked is changed, is a number of code wordassignments not dependent upon the block length L to be checked butmeeting condition given by the expression (2) for an arbitraryinformation sequence.N(L)=N(L−1)  (3)

As seen in FIG. 18, when the code word constraint length is 3 blocks atthe time of decoding, the number N(L) of code word assignments issmaller with the block length L of two than with the block length L ofone. The reason lies in that when an input information sequence isextremely short, there will occur a code word assignment with zero eventthat the state s₀ of the provisional code sequence c₀ coincides with thestate s₁ of the provisional code sequence c₁ and it is regarded that theexpression (2) will not hold for such a code word assignment.

As having been explained above with reference to FIG. 18, in case a DCcontrol bit is inserted fixedly at either the first or second bit of aninformation word in the finite state table in FIG. 15, a total of393,216 code word assignments meeting condition given by the expression(2) exist for an arbitrary information sequence, not depending upon anyblock length to be checked. As mentioned above, however, the number ofcode word assignments meeting condition given by the expression (2) foran arbitrary information sequence is fixed whether a DC control bit isinserted fixedly at any of the first and second bits of an informationword, but all the code word assignments will not be identical to eachother.

Whether the DC control bit is inserted at any of the first and secondbits of an information word, condition given by the expression (2) ismet for an arbitrary information sequence by 196,608 code wordassignments, which is just a half of the aforementioned count “393,216”.

Therefore, when a DC control bit is inserted at either the first orsecond bit of an information word, condition given by the expression (2)is met for an arbitrary information sequence by 3×196,608=589,824 codeword assignments. This number of code word assignments is a total numberof the code word assignments, in the finite state table in FIG. 15, thatmeet condition given by the expression (2), not depending upon any blocklength to be checked. That number of code word assignments is 1/7776 ofall the possible code word assignments in the finite state table in FIG.15.

The 589,824 code word assignments in the finite state table in FIG. 15and meeting condition given by the expression (2), not depending uponany block length, are sorted into three types according to the insertedposition of a DC control bit when condition given by the expression (2)is met for an arbitrary information sequence. The three types include atype 1 indicating a “code word assignment meeting condition given by theexpression (2) for an arbitrary information only when a DC control bitis inserted at the first bit of an information word”, a type 2indicating a “code word assignment meeting condition given by theexpression (2) for an arbitrary information sequence only when a DCcontrol bit is inserted at the second bit of an information word”, and atype 3 indicating a “code word assignment meet condition given by theexpression (2) for an arbitrary information sequence whether a DCcontrol bit is inserted at any of the first and second bits of anarbitrary information sequence”.

FIG. 19 shows numbers of code word assignments of the types 1 to 3 eachwith the code word constraint length of 3 blocks and 4 block,respectively. As shown in FIG. 19, the number of code word assignmentswith the constraint length of 4 blocks is 5 times of that with theconstraint length of 3 blocks, and the code word assignments of thetypes 1 to 3 are identical in number to each other.

Next, three code conversion tables for relative similar code wordassignments resulted from an actual code word assignment in the finitestate table in FIG. 15 will be described with reference to FIGS. 20 to22.

The code conversion table in FIG. 20 is a first example of the finitestate-type 7-state code conversion table of the (1, 7) RLL code.

The code word assignment in the code conversion table in FIG. 20 meetscondition given by the expression (2) for an arbitrary information whenthe code word constraint at the time of decoding is 3 blocks and whethera DC control bit is inserted at the first or second bit of aninformation word. This code word assignment is one of the 32,768 codeword assignments of the type 3 shown in FIG. 19.

The code conversion table in FIG. 21 is a second example of the finitestate-type 7-state code conversion table of the (1, 7) RLL code.

The code word assignment in the code conversion table in FIG. 21 meetscondition given by the expression (2) for an arbitrary information whenthe code word constraint at the time of decoding is 3 blocks and whethera DC control bit is inserted at the first or second bit of aninformation word, as in the code conversion table in FIG. 20. This codeword assignment is one of the 32,768 code word assignments of the type 3shown in FIG. 19. The code conversion table in FIG. 21 is characterizeddifferently from that in FIG. 20, which will be described in detaillater.

The code conversion table in FIG. 22 is a third example of the finitestate-type 7-state code conversion table of the (1, 7) RLL code.

The code word assignment in the code conversion table in FIG. 22 meetscondition given by the expression (2) for an arbitrary information whenthe code word constraint at the time of decoding is 3 blocks and onlywhen a DC control bit is inserted at the first bit of an informationword. This code word assignment is one of the 32,768 code wordassignments of the type 1 shown in FIG. 19. The code conversion table inFIG. 22 is characterized differently from those in FIGS. 20 and 21,which will be described in detail later.

When a 7-bit information sequence “1, 1, 0, 0, 0, 1, 0” is supplied, thecode conversion table in FIG. 21 is updated to meet condition given bythe expression (2) as will be described below with reference to FIG. 23.

When the 7-bit information sequence “1, 1, 0, 0, 0, 1, 0” is supplied,the information sequences d₀ and d₁ having the provisional DC controlbits inserted at the tops thereof, respectively, provisional codesequences c₀ and c₁ resulted from coding of these information sequencesd₀ and d₁ starting with the state 3 according to the code conversiontable in FIG. 21, and code states s₀ and s₁ at the time of coding willbe d₀: 01, 10, 00, 10, c₀: 000, 100, 001, 001 and s₀: 1, 6, 6, 3 and d₁:11, 10, 00, 10, c₁: 000, 010, 101, 001 and s₁: 4, 7, 6, 3, as shown inFIG. 23.

In this example, the states s₀ and s₁ of the provisional code sequencesc₀ and c₁, respectively, are s₀=s₁=6 at a third block, namely, they areidentical to each other. The two's complement q₀ of a sum of the codesequences c₀=“0, 0, 0, 1, 0, 0, 0, 0, 1” up to a time when the codestates become identical to each other is zero (0), while the two'scomplement q₁ of a sum of the code sequences c1=“0, 0, 0, 0, 1, 0, 1, 0,1” up to a time when the code states become identical to each other isone (1). Therefore, the expression (2) holds in this case.

Also in the coding according to the code conversion table in FIG. 21,the expression (2) also holds even when the aforementioned twoprovisional code sequences coincide in state with each other in case aninformation sequence having bits different from the 7 bits 1, 1, 0, 0,0, 1, 0” or in case a DC control bit is inserted at the second bit of aninformation word.

The finite-state code conversion tables in FIGS. 20 to 22 have their owndifferent characteristics. However, the differences among these tablesin FIGS. 20 to 22 will not be easy to understand.

Next, there will be discussed conversion of the finite-state codeconversion tables in FIGS. 20 to 22 into look-ahead code conversiontables, characteristics of the look-head code conversion tables anddifferences among these look-ahead code conversion tables.

Conventionally, a look-ahead code conversion table is converted to afinite-state one as aforementioned, but there is no case that afinite-state code conversion table is converted into a look-head one. Toconvert a finite-state code conversion table into a look-ahead codeconversion table, a code word advanced a necessary look-head amount forcoding should be reassigned to an information word. However, if there isgiven only a finite-state code conversion table, it is not always easyto know the necessary amount of advance for look-ahead. Thus, conversionof a finite-state code conversion table into a look-ahead one is moredifficult than conversion of a look-ahead code conversion table into afinite-state one.

For example, in case a finite-state code conversion table is designedusing the ACH algorithm, it is well known that the maximum amount oflook-ahead advance is a maximum value of each element in an approximatecharacter vector used minus one (1). However, since the value is themaximum amount of look-head advance, it does not always coincide with aminimum necessary amount of look-ahead.

Note here that when the necessary amount of look-head advance fordecoding of a variable-length code conventionally used for coding is Ldblocks, the necessary amount of look-ahead advance for coding is L_(d)/2when the amount Ld is an even number, and (L_(d)1)/2 when the amount Ldis an odd number. A necessary amount of look-ahead advance for decodingcan be known when checking the code word constraint length for decodingon the basis of a finite-state code conversion table.

In the case of a code resulted from coding by the code conversion tablesin FIGS. 20 to 22, the code word constraint length at the time ofdecoding is 3 blocks including a current one. Since the necessary amountof look-ahead advance for decoding is 2 blocks, the necessary amount oflook-ahead advance for coding can be estimated to be one block.

By reassigning a code word advanced one block to an information word inthe code conversion tables in FIGS. 20 to 22 on the basis of the abovefact, the finite-state code conversion tables can be converted intolook-ahead ones, respectively.

The re-assignment of the code word advanced one block to the informationword is such that since in a state 4, an information word preceding theinformation word in consideration is always “11” as in FIG. 21 forexample, a code word “010” created from the state 4 is assigned to theinformation word “11”.

FIG. 24 shows a look-ahead code conversion table for the (1, 7) RLLcode, resulted from conversion of the finite-state code conversion tablein FIG. 20 by re-assigning a code word advanced one block to aninformation word.

FIG. 25 shows a look-head code conversion table for the (1, 7) RLL code,resulted from conversion of the finite-state code conversion table inFIG. 21 by re-assigning a code word advanced one block to an informationword.

FIG. 26 shows a look-ahead code conversion table for the (1, 0.7) RLLcode, resulted from conversion of the finite-state code conversion tablein FIG. 22 by re-assigning a code word advanced one block to aninformation word.

In the look-ahead code conversion tables in FIGS. 24 to 26, the firstcolumn shows supplied information bits and the second column show givencodes. Also, in the tables, (“0”) indicates that a preceding code bit is0 and (“1”) indicates that the preceding code bit is 1.

Next, the characteristics of the look-ahead code conversion tables inFIGS. 24 to 26 will be discussed.

The look-ahead code conversion table in FIG. 24 adopts a paritypreserved (PP) code word assignment given by the expression (1) in whichthe information and code sequences always coincide in parity with eachother. In comparison with the conventional codes shown in FIGS. 7 and 8,the (1, 7) RLL code shown in FIG. 24 is improved in that the number ofstates at the time of coding is decreased from 104 to 7, the code wordconstraint length at the time of decoding is decreased from 5 to 3blocks and the error propagation length at the time of decoding isdecreased from 10 to 6 bits. The code word assignments having similarcharacteristic to that of the code word assignments in the codeconversion table in FIG. 24 count a half of the number of code wordassignments of the type 3 in FIG. 19.

In the look-head code conversion table in FIG. 25, the code wordassignment is done so that when the number of blocks is odd, aninformation sequence will differ in parity from a code sequence and whenthe number of blocks is even, the information sequence will coincide inparity with the code sequence. Apparently, the code word assignment isdifferent from the PP code word assignment given by the expression (1).

In the look-ahead code conversion table, however, the code resulted fromthe code word assignment as in FIG. 25 can undergo the same DC controlas the code resulted from the PP code word assignment having beendescribed with reference to FIG. 24. The reason is that whether thenumber of blocks is odd or even when the code word assignment as in FIG.25, the polarity inversion in a code sequence is assured duringinsertion of a DC control bit. The code word assignments similar incharacteristic to those in the code conversion table in FIG. 25 count ahalf of the code word assignments of the type 3 shown in FIG. 19.

Apparently, the look-ahead code conversion table in FIG. 26 differs thePP code word assignment and also from the code word assignment in FIG.25. In the code conversion table in FIG. 26, a code word assignment isdone for an information sequence including an information word “01” or“11” in the odd-number block so that the information sequence willdiffer in parity from a code sequence and for an information sequenceincluding the information word “01” or “11” in the even-number block sothat the information sequence will coincide in parity with the codesequence.

It is different to apparently judge whether the DC control can be doneefficiently using the code conversion table in FIG. 26. Also in the caseof a code resulted from the code word assignment as in FIG. 26, however,a DC control equivalent to that of the code resulted from the code wordassignment having been described with reference to FIGS. 24 and 25 canbe done by inserting a DC control bit fixedly at the first bit of aninformation word.

As having been described in the foregoing, to meet the condition givenby the expression (1), an information sequence has to coincide in paritywith a code sequence in the look-ahead code conversion table. To meetthe condition given by the expression (2) for the finite-state codeconversion table, the parity of an information sequence may not alwayscoincide with that of a code sequence but it suffices that twoprovisional code sequences should different in parity from each other.That is, the condition given by the expression (2) include that given bythe expression (1).

The code word assignments in the finite-state code conversion table,searched as in the flow chart shown in FIG. 17, include many code wordassignments meeting the condition given by the expression (1) as well asmany ones different from the conventional PP code word assignment havingbeen discussed with reference to FIGS. 25 and 26 when the finite-statecode conversion table has been converted to a look-ahead one.

In the finite-state code conversion table, a code word assignment inwhich that the expression (2) never fails to hold when two provisionalcode sequences coincide in state with each other for an arbitraryinformation sequence will be called “parity-different code wordassignment” and the method of such a code word assignment be called“parity-different code word assignment method” hereunder.

Next, there will be described with reference to FIGS. 27 and 28 theeffect of code spectrum suppression in a low-frequency band when theencoder 51 having been described with reference to FIGS. 11 to 13changes the DC control redundancy by encoding an information sequenceaccording to each of the finite-state code conversion tables having beendescribed with reference to FIGS. 4 and 6 and FIGS. 20 to 22.

More specifically, when a channel clock fc is taken as an index of theeffect of suppressing the low-frequency spectrum of a code, a powerspectral density fc/1024 is used as a typical value of the effect. Also,an operation for determine a spectrum component of fc/1024 by making adiscrete Fourier transform of a code sequence of 4096 bits afterNRZI-modulated was repeated 10,000 times for each of different randominformation sequences, and a mean square was measured.

FIG. 27 shows the dependence of the power spectral density of fc024 onthe DC control redundancy when coding done according to the codeconversion table having been described with reference to FIGS. 4 and 6as well as to FIGS. 20 to 22 with a DC control bit being inserted at thefirst bit of an information word, and FIG. 28 shows the dependence ofthe power spectral density of fc/1024 on the DC control redundancy whencoding done according to the code conversion table having been describedwith reference to FIGS. 4 and 6 as well as to FIGS. 20 to 22 with a DCcontrol bit being inserted at the second bit of the information word.

In case the coding is done according to the code conversion tables inFIGS. 20 to 22 with the DC control bit being inserted at the first bitof the information word, the effect of suppressing the low-frequencyspectrum in a wide range of the DC control redundancy from 0.007 to 0.12as shown in FIG. 27 in comparison with that in a coding according to theconventional finite-state code conversion table.

In case the coding is done according to the code conversion tables inFIGS. 20 to 22 with the DC control bit being inserted at the second bitof the information word, the effect of suppressing the low-frequencyspectrum in a wide range of the DC control redundancy from 0.007 to 0.08as shown in FIG. 28 in comparison with that in coding according to theconventional finite-state code conversion table.

Also, when the coding is done according to the code conversion table inFIG. 22 with the DC control bit being inserted at the first bit of theinformation word, the low-frequency spectrum can be suppressed with ahigh effect as shown in FIGS. 27 and 28. However, when the coding isdone with the DC control bit being inserted at the second bit, theeffect of suppressing the low-frequency spectrum will be lower than in acoding according to the conventional 4- or 5-state code conversion tablefor the reason that the code word assignment is done to meet thecondition given by the expression (2) for an arbitrary informationsequence only when the coding is done according to the code conversiontable in FIG. 22 with the DC control bit being inserted at the first bitof the information word with the DC control bit being inserted at thesecond bit of the information word.

Note however that by making a mutual replacement between a code wordassigned to the information word “01” and a code word assigned to theinformation word “10” or between a code word assigned to the informationword “00” and a code word assigned to the information word “11” in anyof the code conversion tables, a code word assignment when the DCcontrol bit is inserted at the first bit of the information word and acode word assignment when the DC control bit is inserted at the secondbit have their natures thereof completed swapped between them.

That is, in the coding according to the present invention, it is not soimportant whether the DC control bit is inserted at the first bit of aninformation word or at the second bit. The DC control bit should beinserted at the first bit of an information word or at the second bit byselecting a code word assignment capable of a higher effect ofsuppressing the low-frequency band according to the inserted position ofthe DC control bit or according to a code word assignment used.

As will be known from FIG. 27, when coding is done according to the7-state code conversion table in FIG. 21 for example, the redundancy ofthe DC control bit can considerably be improved from 1/22=0.04545 to1/40=0.025 to have a power spectral density of fc/1024 at −8.5 dB, incomparison with that in coding according to the 4-state code conversiontable in FIG. 6. Actually, however, the extent of suppressing the powerspectral density of fc/1024 depends on a system used, but it is usuallyless than −6 dB. Also, the effect of suppressing the code spectrum inthe low-frequency band depends on a DC control method used.

As above, in case DC control bits are inserted in an informationsequence, a code sequence can DC-controlled efficiently by coding theinformation sequence according to the finite-state code conversiontables in FIGS. 20 to 22.

More specifically, in a first example of the coding rule used in theencoder 51 that converts an m-bit information word continuously into ann-bit code word after inserting DC control bits for DC control of a codesequence into an information sequence, when the coding rule isrepresented by a finite-state code conversion table, the informationword is assigned to the code word in the code conversion table so thatwhen the state s₀ of the provisional code sequence c₀ resulted from acoding starting with an arbitrary start-point state on the assumptionthat the DC control bit is 0 becomes the same as the state s₁ of theprovisional code sequence c₁ resulted from a coding starting with thesame start-point state as in the provisional code sequence c₀ on theassumption that the DC control bit is 1, the two's complement of a sumof the provisional code sequences c₀ will always differ from that of asum of the provisional code sequences c₁.

Also, in a second example of the coding rule used in the encoder 51 thatconverts an m-bit information word continuously into an n-bit code wordafter inserting DC control bits for DC control of a code sequence intoan information sequence, under the condition in the above first exampleand also when the coding rule is represented by a look-ahead codeconversion table, the information word is assigned to the code word inthe code conversion table so that when the m-bit information word orn-bit code word is taken as one block and the number of blocks is odd,the two's complement of a sum of the information sequences will alwaysdiffer from that of a sum of the code sequences and when the number ofblocks is even, the two's complement of the sum of the informationsequences will coincide with that of the sum of code sequences.

Also, in a third example of the coding rule used in the encoder 51 thatconverts an m-bit information word continuously into an n-bit code wordafter inserting DC control bits for DC control of a code sequence intoan information sequence, only when the coding rule is represented by afinite-state code conversion table and a DC control bit is inserted atthe first or second bit of a 2-bit information word, the informationword is assigned to the code word in the code conversion table so thatwhen the state s₀ of the provisional code sequence c₀ resulted from acoding starting with an arbitrary start-point state on the assumptionthat the DC control bit is 0 becomes the same as the state s₁ of theprovisional code sequence c₁ resulted from a coding starting with thesame start-point state as in the provisional code sequence c₀ on theassumption that the DC control bit is 1, the two's complement of a sumof the provisional code sequences c₀ will always differ from that of asum of the provisional code sequences c₁.

As having been described in the foregoing, the parity-different codeword assignment method adopted in the finite-state code conversion tableincludes the conventional PP code word assignment method in thelook-ahead code conversion table and provides a lot of code wordassignments outstanding in DC control efficiency other than thoseprovided by the conventional PP code word assignment method. Also incase the parity-different code word assignment in the finite-state codeconversion table results in a PP code word assignment in the look-aheadcode conversion table, the parity-different code word assignment can bedesigned more theoretically. So, a code resulted from theparity-difference code word assignment can have the characteristicthereof improved more than a code resulted from the conventional PP codeword assignment having been described with reference to FIGS. 7 and 8.

Next, there will be described an improvement of the bit error rate whenthe maximum number of minimum runs in sequence of the (1, 7) RLL code isdecreased to less than the conventional number of six (6) and defocusingor tangential tilt has occurred during data reproduction.

FIG. 29 shows the relation between the maximum number of minimum runs insequence and the Shannon capacity in the (1, 7) RLL code. The “Shannoncapacity” is a theoretical maximum coding rate a limited code canattain. A finite-state code conversion table can be designed of a codewhose coding rate less than the Shannon capacity using theaforementioned ACH algorithm.

As will be known from FIG. 29, the maximum number of minimum runs insequence in the (1, 7) RLL code can be reduced to three when the Shannoncapacity is 0.6730 on the assumption that the coding rate is taken as⅔=0.6667.

That is, when a 2-bit information word is continuously converted into a3-bit code word and a coding is done using a coding rule in which theminimum run of a code is limited to one and the maximum run is limitedto seven, the maximum number of minimum runs in sequence of the code islimited to three to five.

Next, there will be described a method of designing a finite-state codeconversion table for the (1, 7) RLL code in case the maximum number ofminimum runs in sequence is five, for example.

FIG. 30 is a 18-state transition diagram and premised on the NRZImodulation and that provides both a (1, 7) RLL code limitation and alimitation of the maximum number of minimum runs in sequence to five.

To set the maximum number of minimum runs in sequence to four in FIG.30, the state transition diagram having the states 17 and 18 deletedtherefrom should be used. When it is desired to set the maximum numberto three, the state transition diagram having states 15 to 18 deletedtherefrom should be used.

First, an approximate character vector “4, 6, 6, 6, 5, 5, 4, 2, 4, 6, 3,6, 3, 5, 3, 5, 2, 3” is derived on the basis of the finite-state statetransition diagram in FIG. 30. Them an 8-state finite state tablesimilar to the 7-state finite state table in FIG. 15 can be designedbased on the approximate character vector and ACH algorithm. FIG. 31shows a finite state table for the (1, 7) RLL code, in which the maximumnumber of minimum runs in sequence is limited to five.

Then, all the (4!)8=110,075,314,176 code word assignments in the finitestate table in FIG. 31 are searched, as in the flow chart in FIG. 17,for code word assignments meeting the condition given by the expression(2), that is, parity-different code word assignments, for an arbitraryinformation sequence, not depending upon a block length to be checked.As a result, the expression (3) holds when L=7 in case a DC control bitis inserted fixedly at the first or second bit of an information word.At this time, there are found 786,432 parity-different code wordassignments. In case the DC control bit is inserted at at least eitherthe first or second bit of the information word, there are found1,179,648 parity-different code word assignments. The number of codeword assignments is 1/93312 of all the code word assignments in thefinite state table in FIG. 31.

However, note here that since the finite state table in FIG. 31 isprepared using the ACH algorithm, which code word assignment is used inthe finite state table in FIG. 31, the code resulted from a coding basedon the code conversion table after the code word assignment can bedecoded by the “sliding block decoding”. The code word constraintlengths at the time of decoding include two: one is 5 blocks and theother is 4 blocks. When the code word constraint lengths at the time ofdecoding is 4 blocks, it includes a code word constraint length of 3blocks at one bit of a 2-bit information word. In such a case, the codeword constraint length remains 4 blocks but the error propagation lengthwill be one bit shorter.

The composition of the 1,179,648 parity-different code word assignmentsin the finite state table in FIG. 31 will be described with reference toFIG. 32. In FIG. 32, the parity-different code word assignments aresorted in 3 types (types 1 to 3 having been described with reference toFIG. 19). Also in FIG. 32, there are stated a code word assignment of 5blocks in code word constraint length and code word assignment of 4blocks in code word constraint length. The parenthesized numbers in FIG.32 indicate the numbers of ones of 3 blocks in code word constraintlength of code word assignments of 4 blocks in code word constraint atone bit of a 2-bit information word.

FIG. 33 shows an example of a finite state-type 8-state code conversiontable for the (1, 7) RLL code, in which the parity-different code wordassignments are included and the maximum number of minimum runs insequence is limited to five. In the code word assignment in the codeconversion table in FIG. 33, the code word constraint length at the timeof decoding is 4 blocks, the code word constraint length at one of thebits of a 2-bit information word is 3 blocks, and the parity-differentcode word assignment will be done whether the DC control bit is insertedt the first or second bit of the 2-bit information word. This code wordassignment is, one of 256 code word assignments of the type 3 shown inFIG. 32.

The code resulted from a coding based on the code conversion table inFIG. 33 is considerably improved as compared with the codes resultedfrom a coding based on the conventional code conversion tables in FIGS.7, 8 and 9. Namely, it has the maximum number of minimum runs insequence thereof decreased from six to five, the number of states at thetime of coding decreased from 1691 to 8, the code word constraint lengthat the time of decoding decreased from 6 blocks to 4 blocks, and theerror propagation length at the time of decoding decreased from 15 bitsto 7 bits.

The code, in which the maximum number of minimum runs in sequence islimited to five by the above coding method of converting a 2-bitinformation word continuously into a 3 bit code word whose the minimumrun is limited to one and maximum run is limited to seven, is superb incharacteristic to a code in which the maximum number of minimum runs insequence is six. In step S6 in FIG. 13, the encoder 51 having beendescribed with reference to FIGS. 11 to 13 makes a coding using a codein which the maximum number of minimum runs in sequence is limited tofive, whereby the number of states at the time of coding, the code wordconstraint length at the time of decoding, and the error propagationlength at the time of decoding, can be reduced to values, respectively,smaller than ever.

Also, in case the coding rule is represented by the finite-state codeconversion table, the number of states can be limited to eight.

Also the finite-state code conversion table in FIG. 33 can be convertedinto a look-ahead one by reassigning a code word advanced 1 block to aninformation word. The resultant look-ahead code conversion table has abasic code conversion table that is the quite same as that shown in FIG.25. Namely, the look-ahead code conversion table thus obtained includesthe basic code conversion table in FIG. 25 and irregular code conversiontable in FIG. 34 added to the latter.

That is to say, the irregular code conversion table in FIG. 34 is addedto the look-ahead code conversion table in FIG. 25 in order to limit themaximum number of minimum runs in sequence to five. According to theirregular code conversion table in FIG. 34, an input information word“10.11” is converted into a code word “000.001” without application ofthe code conversion table in FIG. 25 when a preceding code word is“010”.

In the irregular code conversion table in FIG. 34, the code wordassignment is done for an information sequence to coincide in paritywith a code sequence when the number of blocks is even, as in the codeconversion table in FIG. 25. By making a coding according to a codingrule resulted from addition of the look-ahead irregular code conversiontable in FIG. 34 to the look-ahead basic code conversion table in FIG.25, the maximum number of minimum runs in sequence can be limited tofive while maintaining the parity-different code word assignment. Itshould be noted however that this coding method is equivalent to acoding based on the finite-state code conversion table in FIG. 33.

FIG. 35 shows the results of calculation of the number of code states atthe time of coding, code word constraint length at the time of decodingand error propagation length at the time of decoding in the 7-state codeconversion tables in FIGS. 20 to 22 and 8-state code conversion table inFIG. 33.

By making a comparison between FIGS. 35 and 10, it will be understoodthat the coding method based on the 7-state code conversion tables inFIGS. 20 to 22 and the 8-state code conversion table in FIG. 33 can makea coding with a much more improved number of states at the time ofcoding, code word constraint length at the time of decoding and errorpropagation length at the time of decoding than those attained by thecoding method based on the conventional code conversion tables shown inFIGS. 7, 8 and 9.

Note that any method may be used for decoding the code resulted from theaforementioned coding method according to the present invention. Sincethe code word constraint length at the time of decoding is determined asin FIG. 35, the code resulted from the aforementioned coding may bedecoded by a common sliding-block decoding, for example. Also, since thenumber of states is relatively small in the coding method according tothe present invention, the code may be decoded by a soft decision usingthe Trellis diagram based on the finite-state code conversion table, forexample.

For example, in case a code resulted from a coding based on the codeconversion table in FIG. 21 or 33 is decoded by the sliding-blockdecoding, representation of an input code word sequence of 4 blocks (12bits) by “b0, b1, b2, b3, b4, b5, b6, b7, b8, b9, b10, b11” startingwith the past side permits a very simple circuit to decode a 2-bitinformation word “a0, a1” using the Boolean logic formula given by thefollowing expressions (4) and (5). $\begin{matrix}{a_{0} = {{b_{2}\left( {b_{6} + {\overset{\_}{b_{5}}b_{7}}} \right)} + {b_{4}\left( {b_{6} + b_{7} + {\overset{\_}{x}\overset{\_}{b_{8}}\overset{\_}{b_{9}}\overset{\_}{b_{10}}}} \right)} + \quad{b_{3}b_{5}} + {\overset{\_}{b_{2}}\overset{\_}{b_{3}}{\overset{\_}{b_{4}}\left( {\overset{\_}{b_{1}} + {\overset{\_}{x}\overset{\_}{b_{5}}\overset{\_}{b_{6}}\overset{\_}{b_{7}}}} \right)}}}} & (4) \\{a_{1} = {b_{4} + {\overset{\_}{b_{2}}{\overset{\_}{b_{3}}\left( {b_{0} \oplus b_{5}} \right)}} + {\overset{\_}{b_{5}}\overset{\_}{b_{6}}{\overset{\_}{b_{7}}\left( {\overset{\_}{b_{1}} + b_{3} + x} \right)}}}} & (5)\end{matrix}$

However, when x=0, both codes represented as in FIGS. 33 and 21 can bedecoded, and when x=1, a code represented as in FIG. 21 can be decoded.Also, the bit “b11” is not used in the sliding-block decoding. The DCcontrol bit inserted during coding is normally abandoned at the time ofdecoding.

The aforementioned series of operations can be effected by a software.The software is installed from a recording medium into a computer with adedicated hardware having a program forming the software installedtherein or a general-purpose personal computer in which various programscan be installed and which can perform various functions according tothe corresponding programs.

The recording medium having recorded therein a program under which theaforementioned series of operations is effected is a package mediumincluding a magnetic disk 141 (including a flexible disk), optical disk142 (including CD-ROM (=compact disk-read-only memory), DVD (digitalversatile disk), magneto-optical disk 143 (MD (=Mini-Disk; registeredtrademark)), semiconductor memory 144 or the like as shown in FIG. 16.

Note that in this Specification, the steps of stating a program that isto be recorded to the recording medium include operations effectedtime-serially in their stated order as well as those effected not alwaystime-serially but in parallel or individually.

In the foregoing, the present invention has been described in detailconcerning certain preferred embodiments thereof as examples withreference to the accompanying drawings. However, it should be understoodby those ordinarily skilled in the art that the present invention is notlimited to the embodiments but can be modified in various manners,constructed alternatively or embodied in various other forms withoutdeparting from the scope and spirit thereof as set forth and defined inthe appended claims.

As having been described in the foregoing, the present invention permitsa code conversion. More particularly, in case a coding rule isrepresented by a finite-state code conversion table, the code conversioncan be done under a coding rule by which a code word is assigned to aninformation word so that when a first code state of a first provisionalcode sequence encoded starting with a predetermined start-point statebecomes identical to a second code state of a second provisional codesequence encoded starting with the predetermined start-point state,two's complement of a sum of coding bits included in the firstprovisional code sequence will always differ from that of a sum ofcoding bits included in the second provisional code sequence.

Also, according to another aspect of the present invention, the codingcan be done under a coding rule in which the minimum run is limited toone, maximum run is limited to seven and the maximum number of minimumruns in sequence is three to five.

1-11. (canceled)
 12. A coding method comprising the steps of: generatinga first information sequence by inserting a first DC control bit into aninput information sequence at predetermined intervals and generating asecond information sequence by inserting a second DC control bitdifferent from the first DC control bit into the input informationsequence at the predetermined intervals; generating a first provisionalcode sequence by making a code conversion of the first informationsequence generated in the information sequence generating step at aconversion ratio of an information word length m to an code word lengthn; generating a second provisional code sequence by making a codeconversion of the second information sequence generated in theinformation sequence generating step at the conversion ratio of theinformation word length m to the code word length n; delaying the firstprovisional code sequence and producing a delayed first provisional codesequence; delaying the second provisional code sequence and producing adelayed second provisional code sequence; and selecting either thedelayed first provisional code sequence generated in the first codegenerating step or the delayed second provisional code sequencegenerated in the second code generating step, wherein the first andsecond code converting steps use a coding rule by which, in case thecoding rule is represented by a finite-state code conversion table, codewords are assigned to information words so that a two's complement of asum of coding bits included in the first provisional code sequence isalways different from a two's complement of a sum of coding bitsincluded in the second provisional code sequence when a first code stateof the first provisional code sequence, encoded starting with apredetermined original state, is identical to a second code state of thesecond provisional code sequence, encoded starting with thepredetermined original state. 13-20. (canceled)